The present invention relates to a method for operating an electronic memristive device. Furthermore, the operation of said memristive device for implementing fuzzy logic in the form of an artificial synapse, and the use for implementing all four learning curves of an artificial synapse and of the complementary learning are disclosed.
Memristors or memristive devices are passive electrical devices, the name of which is composed of “memory” and “resistor”. Said devices are characterised in that the resistance state thereof is dependent on the previously applied voltage.
Since the first controlled production thereof in 2007, memristors have been central to device development. Once the first embodiments had been specified digitally, i.e. at binary digital resistance states, memristors were quickly developed that could be specified at a plurality of analoguely defined resistance states, by means of a suitable write voltage.
Apart from special types, such as chemical memristors, memristors used today are formed in the manner of conventional electronic devices. The memristive device may for example comprise a spin-based or magnetic memristor. Said device may also be based on a molecular ionic thin film.
The memristive device comprises two electrically conductive electrodes and a memristive layer sequence (also referred to in the following as a layer sequence). In the following, the term “conductive” will always be used to mean electrically conductive. The memristive layer sequence usually comprises at least one thin film layer (also referred to in the following as a layer), but is usually a succession of mutually cumulative thin film layers that are interconnected in a planar manner. The first and the second electrode contact the memristive layer sequence in an electrically conductive manner and are separated from one another by the memristive layer sequence.
The constituent parts of the memristive device, i.e. the two electrically conductive electrodes and the memristive layer sequence separating said electrodes, are applied by means of known methods of thin-film technology, e.g. by means of PVD processes.
The individual layers of the memristive layer sequence may differ from one another on account of different doping and/or spatial doping distributions. The doping may be base doping or additional doping, for example with metal atoms.
In an embodiment that is frequently used, the thin film layers of the memristive layer sequence are arranged above one another in a horizontal manner. However, any other spatial orientations are also possible, i.e. the layers of the memristive layer sequence may also be arranged for example vertically, side-by-side.
Various material groups are used for producing the memristive layer sequence.
For example, a polycrystalline crystal structure has been found to be a suitable thin film layer structure for memristors having a plurality of resistance states. The polycrystalline memristive layer sequence comprises piezoelectric or ferroelectric layers. According to various embodiments, the ferroelectric layers may comprise a stable base doping that renders the ferroelectric layers semiconductively in nature. The ferroelectric crystal structures may be oxidic. Even without doping agents being introduced, oxidic thin film layers are often intrinsically n-conductive or intrinsically p-conductive.
In a simplest embodiment, a memristive device of this kind comprises a memristive double layer, which has been found to be a particularly suitable thin film layer structure. Said double layer consists of perovskite-like BiFeO3 layers (BFO for short) which are doped with fixed titanium ion donors (BFTO for short) close to one of the electrodes. In this case, the BFO and BFTO layers are thin film layers of the memristive layer sequence. The memristive double layer comprises: first electrode/BFTO/BFO/second electrode.
The electrodes are usually arranged on the outer, mutually opposing faces of the memristive layer sequence and are therefore not directly interconnected in an electrically conductive manner.
In the following, only processes (e.g. the application of voltages) at the first electrode will be considered. Similar processes take place at the second electrode.
Both electrodes are applied to the memristive layer sequence over a large surface area. In a particular embodiment, both electrodes are applied in a selective manner.
The two electrically conductive electrodes are also referred to as the first electrode, terminal 1 (T1), and the second electrode, terminal 2 (T2). In the embodiment used most, the electrodes and the thin film layers of the layer sequence therebetween are formed as horizontal layers, preferably on a substrate. The electrodes are also referred to as a front face electrode (top) or rear face electrode (bottom) electrode or terminal, depending on the position thereof in the horizontal layer sequence, terminal 2 (T2) usually being assigned to the bottom electrode and terminal 1 (T1) usually being assigned to the top electrode.
Layer sequences have proven particularly advantageous in which, when a voltage pulse is applied between T1 and T2 and an electrical field is formed, easily displaceable ions in the layer sequence can be shifted from a region close to the first electrode and into a region close to the second electrode, or vice versa. Since said displacements of ions depend in principle on the direction of the electrical field, the memristive device comprising two electrodes can be operated bidirectionally. Owing to the bidirectional operation, resistance states are written and read, and thus signals are exchanged, in both directions between the electrodes.
Easily displaceable ions move in a directed manner, under the influence of an electrical field, in the crystal lattice. In order for the ion concentrations at the relevant electrode to be maintained in a non-volatile manner, substitutional, invariable and non-displaceable impurity atoms can be implanted into the crystal lattice of the memristive layer sequence. The non-displaceable impurity atoms secure the displaceable ions present up to a critical voltage (write voltage), i.e. up to a critical electrical field strength.
Said non-displaceable impurity atoms are also referred to as “traps” and are caused by the doping of the outer thin film layers of the memristive layer sequence. Traps are place-bound (fixed) energy levels in the region of band gaps of semiconductors, which energy levels can be occupied by electrons.
These are referred to in the following as “fixed traps”. In this case, the traps are distributed in an inhomogeneous manner in the memristive layer sequence.
The fixed titanium traps are already inserted into the interfaces of the memristive layer sequence of the memristive device during production. The fixed titanium traps are thus arranged in the interfaces between the memristive layer sequence and the electrodes. In this case, the interface is in each case to be understood as the outer thin film layer of the memristive layer sequence, which layer borders the adjoining electrode in each case. The fixed titanium traps are inserted during production and accumulation of the BFO layer. Electrically conductive contact can thus be formed at the electrode/BFO interface. In this case, a BFO matrix comprising embedded fixed titanium traps is preferably provided. The titanium doping of the BFO layer cannot be changed by means of an electrical voltage located in the region of the write voltage, and also cannot be changed within the layers.
The titanium traps are inserted for example by means of ion implantation, close to the two electrodes of the outer memristive thin film layers. Further preferred methods for inserting fixed titanium traps are for example laser treatment or thermal diffusion during the accumulation of the BFO layer(s).
The freely movable and displaceable ions are often oxygen vacancies (Vo+, Vo++) which act as hole doping. Said ions act as intrinsically mobile donors and are therefore referred to in the following as mobile oxygen vacancies.
As described in Schmidt et al., the mobile oxygen vacancies are homogenously distributed in the memristive layer sequence.
The position of the mobile oxygen vacancies in the memristive layer sequence can be changed by means of an electrical voltage. During application of a minimum writing voltage for a minimum writing period, the ion cloud of the oxygen ions is shifted from one electrode to the other. This results in the formation of courses of thin film layers having a reduced concentration of oxygen vacancies (depletion layer), or in an increased concentration of oxygen vacancies (concentration layer), on the relevant electrodes.
In the memristive layer sequence based on BFTO/BFO, the mobile oxygen vacancies are shifted into the titanium-doped BFTO layer close to the first electrode, or are shifted out of said layer.
The titanium traps catch the mobile oxygen vacancies in potential wells, which wells can be overcome by a corresponding electrical potential, the minimum writing voltage. The mobile oxygen vacancies are thus captured or released by the titanium traps. Exceeding a minimum writing voltage on one electrode frees the mobile oxygen vacancies from the potential wells of the fixed titanium traps on said one electrode, and allows said vacancies to move in the memristive layer sequence in a directed manner, inter alia towards the other electrode, in order to be recaptured there by fixed traps.
The minimum writing voltage is the voltage that has to be reached or exceeded, in terms of absolute value, in order to achieve a change of state in the memristive layer sequence. If the absolute value of the minimum writing voltage is exceeded, states are written persistently. In a particular embodiment, each minimum writing voltage corresponds to a minimum pulse width tp of a writing pulse used for changing the state. The minimum writing voltage is a threshold value for capturing or releasing the mobile oxygen vacancies in or from the fixed titanium traps.
The minimum writing voltage has to be applied for a minimum time period required by the ions for picking up the drift velocity and travelling the distance between the two electrodes. The minimum writing voltage and the minimum writing period, i.e. the exposure time of the minimum writing voltage are therefore mutually related. The higher the write voltage, the shorter the exposure time thereof can be. The corresponding relationship depends on the material and the doping of the memristive layer sequence, and on the electrode spacing.
Application of a pulse to an electrode is to be understood to mean that the voltage at said electrode is changed from zero. If a voltage pulse is applied to an electrode, said pulse always deviates positively or negatively from zero potential. In a preferred embodiment, a voltage pulse is applied at T1, T2 remaining at zero potential. In a further preferred embodiment, a voltage pulse is applied at T2, T1 remaining at zero potential. According to a third preferred embodiment, the voltage at the first and at the second electrode is changed in opposing directions, meaning that the sum of the absolute values of the voltage gives the absolute value of the resulting voltage. In the fourth preferred case, in which a voltage pulse of the same polarity is applied to the first and the second electrode, the absolute value of the resulting voltage is the absolute value of the difference between the two absolute values of the voltage change.
After the mobile oxygen vacancies have been shifted, i.e. in the non-energised state or below the minimum writing voltage, the ion distributions of the mobile oxygen vacancies are stable. The potential barriers allow for two state on each of the two electrodes at the interface between the memristive layer sequence and the relevant electrode:
ohmic contact (high conductivity) or rectifying Schottky contact (low conductivity). Flexible formation of ohmic contact and Schottky contact on one electrode of the memristive device in each case is described in Schmidt et al., “Big Data ohne Energiekollaps. Physik in unserer Zeit” [“Big data without energy collapse. Physics in our time”], vol. 46, no. 2, 2015, pages 84-89. In this case, the polarity of the voltage applied to the electrodes determines which of the two electrodes is rectifying. This occurs depending on the distribution of the mobile oxygen vacancies, which vacancies drift to one electrode when a voltage is applied, and the fixed titanium traps, which permanently capture mobile oxygen vacancies that drift past in the vicinity thereof.
The mobile oxygen vacancies which have been captured or released by the titanium traps flexibly form potential barriers at the interfaces between the outer thin film layer of the memristive layer sequence in each case, and the relevant electrode adjoining said layer. Applying corresponding electrical voltage pulses makes it possible for the mobile oxygen vacancies to be shifted out of the interface adjoining the first electrode and into the interface adjoining the second electrode.
If mobile oxygen vacancies accumulate at the interface between the memristive layer sequence and the first electrode owing to a first voltage having a first polarity, the potential barrier at the interface adjoining the first electrode is reduced and ohmic contact is established. The second electrode remains at zero potential. At the same time, this leads to depletion of mobile oxygen vacancies at the interface adjoining the second electrode, with the result that the potential barrier at the interface adjoining the second electrode is increased and Schottky contact is established at the second electrode.
If mobile oxygen vacancies accumulate at the interface between the memristive layer sequence and the second electrode owing to a first voltage having a first polarity, the potential barrier at the interface adjoining the second electrode is reduced and ohmic contact is established. The first electrode remains at zero potential. At the same time, this leads to a depletion of mobile oxygen vacancies at the interface adjoining the first electrode, with the result that the potential barrier at the interface adjoining the first electrode is increased and Schottky contact is established at the first electrode.
If mobile oxygen vacancies are depleted at the interface between the memristive layer sequence and the first electrode owing to a first voltage having a first polarity, the potential barrier at the interface adjoining the first electrode is increased and Schottky contact is established.
The second electrode remains at zero potential. At the same time, this leads to a concentration of mobile oxygen vacancies at the interface adjoining the second electrode, with the result that the potential barrier at the interface adjoining the second electrode is reduced and ohmic contact is established at the second electrode.
If mobile oxygen vacancies are depleted at the interface between the memristive layer sequence and the second electrode owing to a first voltage having a first polarity, the potential barrier at the interface adjoining the second electrode is increased and Schottky contact is established. The first electrode remains at zero potential. At the same time, this leads to a concentration of mobile oxygen vacancies at the interface adjoining the first electrode, with the result that the potential barrier at the interface adjoining the first electrode is reduced and ohmic contact is established at the first electrode.
The memristive device may have a surplus or a deficiency of oxygen vacancies at the first electrode/memristive layer sequence interface or at the second electrode/memristive layer sequence interface.
Regarding the potential barrier, the potential barrier is in each case raised just once, at one electrode, while the potential barrier at the other electrode is lowered. The potential barriers can thus be changed in a mutually independent manner. The two potential barriers thus behave in a complementary manner. If no voltage pulse is applied to the electrode T1 (T2 remains at zero potential) or to the electrode T2 (T1 remains at zero potential), or if a non-zero voltage pulse of the same polarity and the same absolute value is applied to both electrodes simultaneously, the potential barriers, and thus also the states, do not change. Raising or lowering the potential barriers simultaneously (which results in the same states being formed at both interfaces) at both electrodes is not possible, owing to the design, since, when a voltage pulse is applied either to T1 (T2 remains at zero potential) or to T2 (T1 remains at zero potential), depending on the polarity of the voltage pulses, the redistribution of the oxygen vacancies establishes either a surplus of oxygen vacancies or a deficiency of oxygen vacancies at T1 and simultaneously a deficiency of oxygen vacancies or a surplus of oxygen vacancies at T2, or a surplus of oxygen vacancies or a deficiency of oxygen vacancies at T2 and simultaneously a deficiency of oxygen vacancies or a surplus of oxygen vacancies at T1.
The potential barrier at one electrode is adjusted so as to be either high or low by means of a correspondingly selected initialisation pulse or writing pulse. Owing to the complementary behaviour, the potential barrier at the other electrode occupys exactly the opposite value, i.e. low or high. For the purpose of digital processing, it is possible to assign the HRS state (high resistance state —low potential barrier) the Boolean value 1, and the LRS state (low resistance state—high potential barrier) the Boolean value 0, or vice versa to assign the LRS state (high potential barrier) the Boolean value 0 and the HRS state (low potential barrier) the Boolean value 1. A resistive switch comprising two reconfigurable potential barriers that can be adjusted in a digitally complementary manner has already been described in You et al.
You et al., Exploiting Memristive BiFeO3 Bilayer Structures for Compact Sequential Logics, Adv. Funct. Mater., 24, 2014, 3357-3365 discloses a resistive switch, the two input variables p and q being represented by an initialisation pulse and a writing process, and it being possible for four resistance states to be adjusted. In this case, the initialisation pulse and the writing process change the resistance state, and the resistance state is read by means of a reading pulse. In this case, the resistive switch nominally consists of a memristive BFTO/BFO double layer comprising two reconfigurable, digitally complementary potential barriers, and two electrodes T1 and T2. The pulse sequences for T1 and T2 consist of an initialisation pulse that is independent of the logical input variables, and an initialisation pulse that is dependent on the logical input variables p and q. This structure consisting of two logical input variables p and q and a reading current output signal, referred to in the following as the current output signal s, makes it possible for all two-valued 16 Boolean functions to be characterised in accordance with a valid truth table, and thus for binary (Boolean) logic to be implemented. In this case, high conductivity of the resistive switch corresponds to the discrete binary output variable 1 of the correspondingly programmed binary logics, and low conductivity of the resistive switch corresponds in this case to the discrete binary output variable 0 of the correspondingly programmed binary logics.
Resistance states correspond to the states that are written to, programmed into, specified in or changed in the memristive device by means of initialisation pulses and/or writing processes. In the following, the term “writing” is used for specifying the resistance states, i.e. resistance states are “written”.
Boolean logic functions (Boolean functions, for short) comprising two logical input variables belong to two-valued Boolean logic and are used in Boolean algebra for example. Said functions are based on binary logical operations and have two clearly defined binary states which occupy either the value 0 or 1. There are 16 two-valued Boolean functions. You et al. discloses the implementation of all 16 two-valued Boolean functions, with reference to a nominal memristive BFTO/BFO double layer.
Fuzzy logic is a form of many-valued logic and a generalisation of (two-valued, binary) Boolean logic, in which the output variables occupy analogue values between 0 and 1. All 16 two-valued Boolean functions have hitherto been characterised by a complementary resistive switch (see You et al.). In contrast to Boolean logic, the output variables in fuzzy logic can occupy any values between 0 and 1. These continuous transitions make it possible to use fuzzy logic for example in artificial intelligence and in control logic for decision-making.
Biological neurons are electrically excitable devices of nerve cells in living organisms. A distinction is made between presynaptic and postsynaptic neurons. In this case, one presynaptic and one postsynaptic neuron, respectively, are interconnected via a synaptic gap. Neurons are used for processing, transmitting and storing information.
In the case of synapses, a distinction is made between chemical and electrical synapses, the chemical synapses being the most common type: In the case of electrical synapses (gap junctions), the presynaptic and postsynaptic neurons are close together at specific points, with the result that signal transmission across a plasma bridge can occur via special ion channels. Action potentials thus propagate relatively quickly and synchronously.
In the case of chemical synapses, there is no direct contact between the neurons. The excitation transmission takes place through a 20 to 30 nm wide synaptic gap which is bridged by means of emission and attachment of messenger substances and neurotransmitters. In this case, signal transmission always occurs in one direction (unidirectional conductivity) from the presynaptic to the postsynaptic neuron.
The plastic change in the conductivity of the chemical synapses is referred to as STDP (spike time depending plasticity). Non-volatile conductivity changes between presynaptic and postsynaptic neurons form in the brain in order, for example, to store information. The STDP also defines inter alia the signal transmission of chemical synapses, which transmission is dependent on a temporal offset Δt (spike timing) between the pre- and postsynaptic signal.
The synaptic weight (synapse strength) refers to the strength for a synaptic connection and characterises the transmission behaviour of synapses. The synaptic weight is shown as a function of the temporal offset Δt between the pre- and postsynaptic signal, in a Cartesian coordinate system.
The long-term boosting of the signal transmission is referred to as long-term potentiation (LTP), whereas the long-term weakening of the signal transmission is referred to as long-term depression (LTD).
The learning curve of a chemical synapse is described by the long-term potentiation, as a function of the temporal offset Δt between the presynaptic and postsynaptic activity. Each chemical synapse has two learning curves: LTP and LTD, the LTP curve also being referred to as a forgetting curve.
Artificial neurons are electronic devices which physically replicate the functionality of biological neurons. Said neurons are for example implemented by memristors or memristive devices comprising two electrodes.
Similar to the biological synapses, each artificial synapse has LTP and LTD learning curves. Said curves are implemented by applying STDP pulses, consisting of temporally offset pre- and postsynaptic writing pulses, to the two electrodes of the memristive device. In order to approximate the mode of operation of biological synapses, the pulse sequence is applied repeatedly approximately 60 to 80 times (multiple pairing). Du et al. shows that it is sufficient to apply the pulse sequence once to the artificial neurons (single spike pairing) and to thus increase energy efficiency.
Du et al., Single pairing spike-timing dependent plasticity in BiFeO3 memristors with a time window of 25 ms to 125 μs, Front. Neurosc., 9, 2015, 227 discloses a resistive switch comprising a flexible analogue non-complementary potential barrier that acts as an artificial synapse, the two electrodes each forming artificial neurons. A flexible analogue non-complementary potential barrier is formed at the Ti/Pt bottom electrode by means of titanium traps thermally diffusing into the lower part of the BFO layer during BFO accumulation on the Ti/Pt bottom electrode, and thus being incorporated in a substitutional and invariable manner. The synaptic weight of the resistive switch is determined depending on the temporal offset Δt between the presynaptic pulse and the postsynaptic pulse. The resistive switch makes it possible for analogue switching to be achieved by means of a single writing pulse sequence. Furthermore, two learning curves, LTP and LTD, can be plotted. The pulse sequence applied at the electrodes or neurons consists of an initialisation pulse followed by two temporally mutually offset writing pulses of different polarities, and a following reading pulse. Said pulse sequence is applied just once to the electrodes or neurons, and not, as in previous publications, 60 to 80 times, resulting in a significant time advantage and also reducing energy consumption.
The use of memristors or memristive devices in the fields of semiconductor electronics is developing steadily. The particular arm in this case is to implement Boolean functions using just one resistive device. This could not only establish a connection to current digital technology, but also contribute to miniaturisation of the devices. Furthermore, there are indications of uses in analogue electronics, fuzzy logic, and the replication of biological stimulus transmission and stimulus processing.
A disadvantage is that, owing to the design thereof and/or the operating and actuation methods used to date, the memristive devices of the prior art (in You et al. and Du et al.) can implement fuzzy logic only for selected Boolean functions, but not for all 16 two-valued Boolean functions.
Furthermore, it is currently possible to read out only one resistance state in each case of a state pair containing mutually complementary resistance states. This excludes the possibility of implementing all four learning curves. To date, only two learning curves (LTP and LTD) have been implemented, which curves characterise STDP behaviour. The anti-LTP and anti-LTD learning curves, complementary thereto, for the anti-STDP behaviour cannot be depicted. It is thus also not possible to easily read out mutually complementary states.
A further disadvantage is that the use of the memristive device is restricted by the prior art. The memristive device cannot be used universally, which would be desirable when processing complementary information from image analysis or speech recognition for example. The known methods for operating memristive devices are not sufficient for use in neuronal networks or control systems either.